# Catalytic cracking problem

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Catalytic cracking problem | |
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State dimension: | 1 |

Differential states: | 2 |

Discrete control functions: | 1 |

Interior point equalities: | 2 |

This problem tries to determine "reaction coefficients for the catalytic cracking of gas oil into gas and other byproducts." (Cite and problem taken from the COPS library)

## Mathematical formulation

The problem is given by

**Failed to parse (unknown function "\norm"): \begin{array}{llcl} \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} \norm{y(\tau_j; \theta) - z_j}^2 \\[1.5ex] \mbox{s.t.} & \dot{y}_1 & = & -(\theta_1 + \theta_3) y_1^2, \\ & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\ \end{array} **

## Parameters

The values are measurements for the concentration for at time points .

## Source Code

Model descriptions are available in